What is the square root of 149?
Understand the Problem
The question is asking for the square root of the number 149, which is a mathematical operation that finds a number that, when multiplied by itself, gives 149.
Answer
The square root of 149 is approximately $12.2066$.
Answer for screen readers
The square root of 149 is approximately $12.2066$.
Steps to Solve
- Identifying the square root operation
To find the square root of a number, you can use either multiplication or a calculator function. The square root of a number $x$ is the number $y$ such that $y^2 = x$.
- Applying the square root to 149
To compute the square root of 149, we can either estimate it between two perfect squares or use a calculator.
We know that:
$$ 12^2 = 144 $$
and
$$ 13^2 = 169 $$
Thus, the square root of 149 lies between 12 and 13.
- Using a calculator for precision
Using a calculator, we find:
$$ \sqrt{149} \approx 12.206555615733702 $$
This provides a more accurate value for the square root of 149.
The square root of 149 is approximately $12.2066$.
More Information
The square root of 149 is an irrational number. This means it cannot be expressed as a simple fraction. The decimal expansion continues infinitely without repeating, making it non-terminating.
Tips
- Forgetting that the square root can be irrational: Many may assume that all square roots yield whole numbers, but this is not always true.
- Not verifying the result: After finding the square root, it's important to square the answer to ensure it equals the original number.
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